Question

The third term of a G.P is square of its first term and the fifth term of it is 64 . find the sum of the first six terms of the GP

Answer 1

The third term of a GP = square of its first
term
ar^2 = (a)^2
r^2 = a^2÷a
r^2 = a .......(1)
now it is given that 5th term is 64 so
ar^4 = 64
a(r^2)^2 = 64
from eq (1)
a(a)^2 = 64
a^3 = 64
a = 4
now from eq (1)
r^2 = a
r = a^(1/2)
r. = 4^(1/2)
r. = 2
now we have a and r so we can calculate the first six terms of the GP.
The first six terms if the GP are

a, ar, ar^2, ar^3, ar^4, ar^5
now putting the value if a and r we have first six terms of the GP
So the terms are

4, 8, 16, 32, 64, 128

Answer 2

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